JOURNAL OF FERMENTATION AND BIOENOINEERING Vol. 79, No. 1, 54-58. 1995
Use of Chemostat Data for Modelling Extracellular-Inulinase
Production by
Kluyveromyces marxianus in a
High-Cell-Density
Fed-Batch Process
MARCO C. M. HENSING,’ JOHANNES S. VROUWENVELDER,’ CHRIS HELLINGA,
JOHANNES P. VAN DIJKEN,’ AND JACK T. PRONK’*
Department of Microbiology and Enzymology’ and Department of Bioprocess Engineering,2 Kluyver Laboratory of Biotechnology, Delft University of Technology, Julianalaan 67, 2628 BC Delft, The Netherlands
Received 18 June 1994IAccepted 4 November 1994
Production of extracellular inulinase by low-cell-density (2 kg dry weight -rnm3) sucrose-limited chemostat cultures of Kluyveromyces marxianus obeyed saturated kinetics at dilution rates ranging from 0.02 to 0.5 h-l. A non-structured Monod-type equation, describing the relation between specific growth rate and specific extracellular-inulinase production rate, was used to fit experimental data. This equation was subsequently incorporated in a model for the production of biomass and extracellular inulinase in a high-cell-density (> 100 kg dry weight .rnm3) fed-batch culture of K. marxianus grown on sucrose. The model adequately described biomass production in the fed-batch culture. However, the production of extracellular inulinase in the fed- batch process was slightly higher than predicted by the model. This observation may be related to differences in growth conditions between in the chemostat and fed-batch cultures.
[Key words: modelling, chemostat, extracellular inulinase, Kluyveromyces marxianus, fed-batch process]
Fed-batch fermentation is commonly employed for large-scale industrial processes involving bacteria, filamentous fungi and yeasts (1). Volumetric productivity (kg product.m-3.h-‘) is a often a key factor in deter- mining the economic viability of such processes. One way to improve volumetric productivity is the applica- tion of high biomass densities.
The development of single-cell protein processes has given a strong impetus to the development of high-cell- density processes for the cultivation of microorganisms (Wegner, E. H., US patent 4414329, 1981). A novel field in which high-cell-density fermentation is required is the production of heterologous proteins (2). Currently, proc- esses for the cultivation of yeasts at biomass concentra- tions exceeding 100 kg.mp3 have been described for a number of yeasts, including Hansenula polymorpha (3), Pichia pastoris (4) and Saccharomyces cerevisiae (5).
To avoid problems arising from limited cooling and oxygen-transfer capacities of industrial bioreactors, high- cell-density fed-batch cultivations are characteristically performed at a low and often decreasing specific growth rate. For the modelling of such processes and to achieve maximum productivity within the constraints imposed by limited oxygen- and heat-transfer capacity of industrial bioreactors, it is essential to know the relation between the specific growth rate (p) and the specific rate of prod- uct formation (qp) (6, 7). Chemostat cultivation is a com- monly used and powerful tool to study the growth-rate dependency of microbial processes. Under steady-state conditions, the specific rate of product formation (qp) follows from Eq. 1.
qp=D*Cp*C;’ (1)
However, there are few studies in which data obtained in laboratory chemostat cultures have actually been used to predict growth and product yields in high-cell-density
* Corresponding author.
fed-batch processes.
The aim of the present paper was to assess the applicability of chemostat data for the modelling of growth and production of the extracellular enzyme in- ulinase (P-2,1-D-fructanfructanohydrolase; EC 3.2.1.7) by Kluyveromyces marxianus in a lOO-liter-scale fed- batch process, at cell densities exceeding 100 kg .m-3. To this end, chemostat data were used for the formulation of an empirical relation between growth rate and prod- uct formation. Growth and product formation predicted by a model based on the chemostat data were compared with those observed in an actual high-cell-density fed- batch process, taking into account the non-negligible volume occupied by cells at high biomass densities.
MATERIALS AND METHODS
Microorganism and maintenance K. marxianus var. marxianus CBS 6556 was obtained from the Yeast Division of the Centraalbureau voor Schimmelcultures (CBS), Delft, The Netherlands and maintained on YEPD-agar slopes. YEPD contained per liter of deminer- alized water: yeast extract (Difco, MI, USA), log; Bacto-peptone (Difco), 20g; and glucose, 20g.
Chemostat cultivation Aerobic, sucrose-limited chemostat cultivation was performed at 40°C in Ap- plikon laboratory fermentors with a working volume of 1 1. The cultures were sparged with air (11. min-‘) and stirred at 800 rpm. The dissolved-oxygen concentration, measured with a polarographic electrode (Ingold), re- mained above 50% of air saturation. The culture pH was controlled at 4.5 by the automatic addition of 1 mol. 1-l KOH. The mineral medium contained per liter of demineralized water: (NH&S04, 5 g; MgS04.7H20, 0.5 g; KH2P04, 3 g; EDTA, 15 mg; ZnSO,. 7H20, 4.5 mg; MnCl,. 7Hz0, 1 mg; COC~~.~H~O, 0.3 mg; CuS04.5H20, 0.3 mg; NaMoO,.2H,O, 0.4 mg; CaCl,- 2Hz0, 4.5 mg; FeS04.7H20, 3mg; H,BO,, 1 mg; KI, 54
VOL. 79. 1995 MODELLING OF INULINASE PRODUCTION IN FED-BATCH PROCESS 55
0.1 mg; biotin, 0.1 mg; calcium pantothenate, 1 mg; nico- tinic acid, 1 mg; silicon antifoam agent (BDH, Poole, UK), 0.15 ml. The medium was sterilized at 120°C for 20 min. Sucrose (CSM, Amsterdam, The Netherlands) was sterilized separately at 110°C for 20 min and added to a final concentration of 5 kg.me3.
Determination of cell number and cell volume sam- ples from a sucrose-limited chemostat culture, grown at a dilution rate of 0.2 h-l, were diluted in Isoton buffer (Coulter Electronics, Harpenden, England) and counted with a Casy 1 model TTC Cell Counter and analyzer system (Scharfe System, Reutlingen, Germany). For cell volume distribution assays, the apparatus was calibrated with 8.7 pm latex beads (Coulter Electronics). A spheri- cal cell shape was assumed for cell-volume estimates.
Fed-batch fermentation Fed-batch cultivation was performed in an Applikon fermentor with a working volume of 100 1, at 40°C and at an impeller speed of 800 rpm. During fermentation, the dissolved-oxygen concentration in the fermentor was kept above 30% of air saturation by sparging with mixtures of air and oxygen. The pressure in the fermentor was adjusted manually up to a maximum of 2.5 bar. The culture pH was con- trolled at 4.5 by the automatic addition of 7.5 mol.l- I NH40H. The medium feed was continuously monitored by following the weight of the fermentor and the reser- voir vessels, all of which rested on electronic balances.
The fermentor, containing 30 I of two-fold concentrat- ed mineral medium (see above), was steam-sterilized (45 min at 12O’C). After inoculation, sucrose was added to give a concentration of lOg.f-I. The culture was in- oculated with cells from a sucrose-limited chemostat cul- ture grown at a dilution rate of 0.10 h-l. During batch growth, the aeration was automatically adjusted to keep the dissolved-oxygen concentration above 50% of air saturation. After depletion of sucrose, indicated by a steep rise of the dissolved-oxygen concentration and a drop in oxygen consumption and carbon-dioxide produc- tion, the fed-batch phase was initiated.
The medium feed used in the fed-batch phase con- tained per liter of demineralized water: (NH,)$04, log; MgSO,.7H,O, 5 g; KH2P04, 20 g; EDTA, 0.75 g; ZnS0,.7H,O, 0.225 g; MnC12.7H,0, 0.05 g; CoC&. 6H,O, 0.015 g; CuS04.5H20, 0.015 g; NaMoO,.2H,O, 0.02 g; CaCl,.2H,O, 0.225 g; FeS04.7H20, 0.15 g; H3B03, 0.05 g; KI, 5 mg; calcium pantothenate, 0.1 g; nicotinic acid, 0.1 g; Struktol 5673 antifoam agent (Struktol Co., Stow, USA), 0.13-0.33 ml (depending on the biomass concentration in the fermentor). Sucrose was present in the feed medium at a concentration of 500 kg.mw3. Medium components were dissolved in sterile demineralized water, but not autoclaved. Micro- scopic examination did not reveal contamination during the fed-batch cultivation. The medium was pumped into the reactor from 20-l reservoir vessels, using a con- trollable Watson-Marlow 503U pump (Watson-Marlow, Falmouth, UK) with flow rates ranging from 0.2 to 4.8 I.h-I. The growth rate was kept at 0.20 h-* until a dissolved-oxygen concentration of 30% air saturation could no longer be maintained. At this stage, the feed was kept constant. A personal computer with ONSPEC software (Heuristics, Sacramento, USA) was used to control the medium pump. The feed rate (F,) required to maintain a constant specific growth rate was program- med according to Eq. 2.
TABLE 1, Values of key parameters used for modelling of growth and extracellular-inulinase production in high-cell-density
fed-batch cultures of K. marxianus CBS 6556
Parameter Svmbol Default value Reference
Initial volume Initial biomass concentration Substrate requirement for maintance Sucrose concentration in feed
Specific cell volume Biomass yield on sugar Specific rate of product
formation Linear feed VO 35.2.10--3m3 Cxll 4.5 kg.m3 m, 0.024 kg.kg-‘.h-’ (13) C,, 500kg.m 3 V wff 2.15. 10m3 mj. kg ~I This study Y,X 0.4Okg.kg ’ (9) % Eq. 2 F,i, 4.77, lo-! m3. h ’
Symbols and values of process parameters are given in Table 1. A detailed description of the development of this fed-batch process will be published elsewhere (8).
Inulinase assay Extracellular-inulinase activity was assayed in culture supernatants as described by Rouwen- horst et al. (9). Enzyme activities were converted to amounts of inulinase protein by using a specific activity of pure supernatant inulinase of 1,500 U (mg inu- linase))’ (10).
Stability of supernatant inulinase At the end of the fed-batch process, a culture sample was centrifuged (10 min at 10,OOOg). Sodium azide (0.04%) was added to the supernatant, which was subsequently filter-sterilized (0.2/1m Acrodisc, Gelman) and incubated at 40°C. Over a period of 100 h, samples were aseptically withdrawn for assaying inulinase activity.
Computer-assisted simulations Numerical solutions of models for fed-batch fermentation were calculated using the simulation program PSI/C (Boza, Pijnacker, The Netherlands).
RESULTS
Effect of growth rate on inulinase production by su- crose-limited chemostat cultures Independent of the growth conditions, approximately 50% of the total inu- linase content of K. marxianus cultures is excreted into the growth medium (9, 11). Measurement of intracellular and cell-wall-associated inulinase was not included in the present study. Previous work on inulinase production by
K. marxianus CBS 6556 in chemostat cultures has indi-
cated that the highest inulinase production occurred in sucrose-limited chemostat cultures (9). Because sucrose, which is also the major carbon source in molasses, is highly soluble and cheap, it is an attractive feedstock for large-scale fermentations. It was therefore decided to use sucrose as a carbon and energy source in all experi- ments.
In sucrose-limited chemostat cultures of K. marxianus, the specific rate of enzyme production qp has been re- ported to depend strongly on the specific growth rate (9) and, at specific growth rates below 0.5 h-l, appeared to follow saturation kinetics (Fig. 1). Even if detailed knowledge on the regulation of inulinase synthesis were available, a structured model would probably have to involve a large number of parameters and equations,
56 HENSING ET AL. 3.0 2.5 i 4 2.0 i ," 1.5 9 1.0 6 0.5 0 0 0.1 0.2 0.3 0.4 0.5 D lh-‘I
FIG. 1. Relationship between dilution rate (specific growth rate)
and specific rate of extracellular-inulinase production by aerobic,
sucrose-limited chemostat cultures of K. marxianus CBS 6556 [data
recalculated from (9)]. Growth conditions: T=40”C, pH 5, C,,=S
kg sucrose.m-3. Inulinase production rates (g inulinase. [kg dry
weight]-‘. h-t) were calculated from enzyme activities using a specific activity of pure inulinase of 1,500 U. (mg inulinase))’ (10). The line drawn through the data points is the best fit to a Michaelis-Menten-
type satured-production-kinetics equation, calculated with the com-
puter program Fig. P (Fig. P Software Co., Durham, USA).
thereby complicating its use for process optimization. Furthermore, the regulation of the INUI gene (12, 13) has not yet been studied in detail at the molecular level. An empirical approach was therefore followed to de- scribe the kinetics of extracellular-inulinase production. The extracellular-inulinase-production rates observed in sucrose-limited chemostat cultures grown at dilution rates between 0.02 h-r and 0.50 h-r (9) were fitted with a Michaelis-Menten-type equation (Fig. 1). This resulted in the empirical description of qp presented in Eq. 3:
Equation 3 was subsequently used to predict extracellu- lar inulinase production in a high-cell-density fed-batch process.
The specific volume (Vspec) of K. marxianus was mea- sured in cells sampled from a sucrose-limited chemostat culture grown at a dilution rate of 0.20 h-l. I/spec of these cells was 2.15 X 10e3 m3. (kg biomass))‘, implying that at a biomass concentration of 100 kg.m-3, over 20% of the culture volume will be occupied by the yeast cells. When production of an extracellular enzyme is studied in high-cell-density cultures, the volume occupied by biomass clearly cannot be neglected.
Stability of supernatant inulinase The product con- centration in a fed-batch process is the net result of prod- uct formation, dilution and degradation. For modelling of the overall process, it is essential to know the kinetics of product degradation. Therefore, the rate of extracellu- lar-inulinase degradation was investigated under process conditions. Cell-free supernatant, harvested at the end of a high-cell density fed-batch fermentation showed no loss of activity after incubation for 100 h at 40°C (data not shown). Since the fed-batch fermentations took less than one third of this time, absolute stability of inulinase was assumed.
Modelling of extracellular-inulinase production during fed-batch cultivation Growth and production of extracellular inulinase by K. marxianus during growth in fed-batch cultures were modelled by a series of standard
J. FERMENT. BIOENG., equations, which are briefly described below.
The change of the biomass concentration in the fer- mentor is the net result of growth and the dilution caused by the medium feed. Thus, the increase of the amount of biomass can be described by Eq. 4.
r,= II+- *C,*V
( 1 (4)
During the exponential feed phase, the specific growth rate was kept constant at 0.20 h-r by manipulating the medium flow rate according to Eq. 2 (see methods sec- tion). When this growth rate could no longer be main- tained due to the limited oxygen-transfer capacity of the reactor, the culture was switched to a constant feed. A constant feed rate will result in a lower specific rate of substrate consumption and, consequently, in a decrease of the specific growth rate. This effect is augmented by the relatively high energy requirement for maintenance at low specific growth rates. The effect of the feed rate on the specific growth rate is described by Eq. 5.
~= (Csi*Fs-ms*~CJ*Ysx
v*G (5)
During fed-batch cultivation, the biomass concentration and the culture volume increase according to Eqs. 6 and 7, respectively.
C =&*C X V x0 V I rdt +- 1 X (6) V= V,+
I F,dt (7)
The volume occupied by the biomass is the product of the biomass concentration, the culture volume and the specific volume of the biomass (m-3. [kg dry weight]-‘; Eq. 8).
Kell =
(CX * y* Vspec) (8)The rate of product formation by the culture is equal to the product of the biomass concentration, the specific rate of product formation and the culture volume (Eq. 9).
rp=qp*CX*V (9)
The product concentration in the fermentor is a func- tion of the initial product concentration, the rate of prod- uct formation and the volume of the culture (Eq. 10). Finally, correction for the volume occupied by the cells gives the product concentration in the extracellular fluid (Eq. 11). V C =O*C,+$ p v s r,dt (10) * C P. ext = ( v5 v!,,, (11)
Verification of the model The Eqs. 2-l 1 were numer- ically solved to predict growth and product formation in a sucrose-limited fed-batch fermentation of K. marx- ianus. After an exponential growth phase at ~=0.20 h-l, the culture was switched to a constant feed, which was expected to cause a progressive decrease of the growth rate to below 0.07 h-r (Fig. 2A). This decrease of the growth rate caused a decrease of qp by approxi- mately 50% in the sucrose-limited chemostat cultures
VOL. 19, 1995 MODELLING OF INULINASE PRODUCTION IN FED-BATCH PROCESS 57 Time Ihl 125 25 110
-B
;
100 Time lhl 0 10 20 30 Time [hlFIG. 2. Comparison of experimental data obtained in a high-
cell-density fed-batch fermentation of K. marxianus CBS 6556 (sym-
bols) with results predicted by numerical solution of the Eqs. 2-11
(solid lines). The exponential-feed phase was initiated after 6.3 h
(dashed line). After 23 h, a constant feed of 4.77 1. h-i was applied.
Further process parameters are presented in Table 1. (A) Pro-
grammed medium feed (F,) and specific growth rate (,e); (B) culture volume (V) and culture dry weight (C,); (C) extracellular inulinase concentration (C,).
(Fig. 1).
The observed biomass concentration and culture volume closely followed the pattern predicted by the model (Fig. 2B). This was essential, because one of the aims of this experiment was to test the assumed relation between specific growth rate and enzyme production. Only during the final hours of the process, the measured biomass concentrations, which exceeded 115 kg. mP3, were slightly lower than predicted by numerical solution of the model (Fig. 2B). This may reflect an inaccuracy in the assumed maintenance-energy requirement, which had been derived from literature data (Table 1).
The amount of extracellular inulinase at the various stages of the fed-batch process was predicted on the basis of Eq. 3, derived empirically from data obtained with low-biomass-density (2 kg.m-3) chemostat cultures. From the results presented in Fig. 2C, it appears that the
observed enzyme production was slightly higher than predicted by numerical solution of the Eqs. 2-11.
DISCUSSION
The present study clearly illustrates that chemostat cul- tivation can be used to obtain the key parameters needed for modelling of high-cell-density fed-batch processes. The unstructured model described by the Eqs. 2-11 ade- quately predicted biomass formation in a high-cell-den- sity fed-batch fermentation of K. marxianus (Fig. 2). The observation that the concentration of extracellular inu- linase was consistently about 20% higher than predict- ed (Fig. 2C) may be due to the different ionic composi- tion of the medium used for fed-batch cultivation. This medium, although derived from the chemostat medium, was not extensively optimized. For example, the fed- batch medium contained rather high concentrations of EDTA, which may affect the distribution of inulinase over cell wall and extracellular medium (10). Other fac- tors that affect cell structure, including the elevated pres- sure applied in the fed-batch fermentation, may also be of importance in this respect. Furthermore, refinement of models based on chemostat cultures will have to take into account the dynamic nature of fed-batch fermenta- tions which, in contrast to chemostat cultures, cannot be considered to be in steady state. In particular the relaxa- tion time of product formation in response to a de- creasing growth rate is an important parameter in this respect (15). Transient-state experiments using chemostat cultures may provide quantitative data applicable in even more reliable models.
In principle, the strategy used in the present study can also be applied for modelling heterologous-protein pro- duction. However, the large number of generations in- volved in chemostat cultures requires that expression vec- tors used for such studies be extremely stable. Unfor- tunately, this is not the case for most episomal vectors currently available for the expression of heterologous proteins in yeasts (3). Techniques for the multi-copy in- tegration of expression cassettes in the yeast genome combine a high copy number with a high mitotic stabil- ity (3, 16). Such vectors have been used to study the relationship between growth rate and specific product formation rates of heterologous a-galactosidase in the yeasts S. cerevisiae and H. polymorpha (17). When the simple model presented in this paper is adapted by including an empirical p-versus-q, relation and the relevant physiological parameters, it should be directly applicable to other wild-type and genetically engineered strains.
NOMENCLATURE
G : product concentration, kg product. m-3
c P, ext : product concentration in extracellular medium, kg product. rnp3
G : substrate concentration in reactor, kg substrate. mP3
csi : substrate concentration in feed, kg substrate.m-3 CX : biomass concentration, kg dry weight .m-3 D : dilution rate, h-i
F, : feed rate, m3. h-i P : specific growth rate, h-i
171, : substrate requirement for maintenance, kg sub- strate. (kg dry weight)-‘. h-i
58 HENSING ET AL. J. FERMENT. BIOENG..
4P : specific rate of product formation, kg product. (kg dry weight)-‘. h-l
rP : rate of product formation, kg product. h- * rx : rate of biomass production, kg dry weight. h-l
V : culture volume, m3
V cell : volume occupied by biomass, m3
V spec : specific volume of biomass, m3. (kg dry weight)-] vo : initial culture volume, m3
YSX : biomass yield on substrate, kg dry weight .(kg substrate)-’
7.
8.
9.
ACKNOWLEDGMENT
This research was sponsored by the Dutch Ministry of Economic Affairs and by Unilever Research Vlaardingen.
10.
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